I do wonder, however, if there were potential patients available, who were near death solely due to the need for a heart transplant (and were near-certain not to get a conventional human transplant in time), and not also because of a host of other issues.

Given the complexities of the human body and how central strong circulation is to them, "Near death from heart failure, ineligible or outside the window for another transplant, but lacking any life-threatening non-cardiac comorbidities" is going to be a tough find.